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Annuity  Studies 


— BY— 

Samuel  F.  Racine 

Certified  Public  Accountant 


COPYRIGHT  1919 

BY 

SAMUEL  F.  RACINE 


MAI.N  LiCi^ARY 


PUBLISHED    BY 

THE  WESTERN  INSTITUTE  OF  ACCOUNTANCY 
COMMERCE  AND  FINANCE 

LEARY  BLDG.  SEATTLE,  WASH. 


Accounting  Students'  Series 

Graded  Corporation  Problems,  1914  and  1918;  containing 
the  most  severe  C.  P.  A.  examination  problems  used  up  to  the 
year  of  publication,  1914;  since  revised  and  brought  down  to 
date,  1918.     Price  $1.50. 

Guide  to  the  Study  of  Accounting,  1916 ;  similar  to  the 
preceding  Guide  to  the  Study  to  Accounting,  but  practically  a  new 
book,  owing  to  the  advent  of  new  books  of  recognized  authority. 
Price  $1.25 

Guide  to  the  Study  of  Auditing,  1916.  The  publication  of 
a  new  Montgomery's  Auditing  required  that  the  original  Guide  to 
Auditing  be  rewritten,  hence  the  1916  book.     Price  1.25. 

Practical  Problems,  Series  "A,"  1916 ;  containing  the  great 
majority  of  the  C.  P.  A.  examination  questions  used  in  the  State 
of  Washington.  This  book  has  been  revised  three  times.  Price 
$1.50. 

Accounting  Principles,  1917.  A  new  book  originally  writ- 
ten in  1913,  containing  much  subject  matter  not  found  in  other 
books  on  accounting.  Assuredly  it  contains  more  information 
than  any  other  single  book  on  the  subject.     Price  $3.00. 

Annuity  Studies,  1918;  a  set  of  rules  easy  to  understand, 
with  problems  on  annuities.     Price  $1.00. 

Syllabus  of  Bookkeeping,  1918.  As  with  all  of  Mr.  Racine's 
books,  originality  is  the  keynote  of  the  Syllabus  of  Bookkeeping. 
There  is  nothing  else  like  it  in  print.  It  is  hoped  that  it  will 
simplify  the  method  of  instruction  in  bookkeeping  to  an  extent 
not  considered  possible  by  other  instructors  of  the  present  day. 
It  is  designed  to  combine  the  advantages  of  lectures  with  the  other 
usual  methods  of  bookkeeping  instruction  and  is  proving  a  decided 
success  in  the  class  rooms  of  The  Western  Institute  of  Account- 
ancy, Commerce  and  Finance. 


/f   /^  P^  «>  r-fc    * 


^  ^  :  jThe  Accumulation  of  $1.00  at  Compound  Interest 


ERIOD 

s    1% 

'  i'A%~ 

1/2% 

2% 

2^% 

2y2 

0 

1 

2 
S 
4 

1. 

1.01 

1.0201 

1.030301 

1.04060401 

1. 

1.0125 
1.02515625 
1.03797070 
1.05094534 

1. 

1.015 
1.030225 
1.04567838 
1.08136355 

1. 

1.02 

1.0404 

1.061208 

1.08243216 

1. 

1.0225 

1.04550625 

1.06903014 

1.09308332 

1. 

1.025 
1.050625 
1.07689063 
1.10381289 

6 
6 

7 
8 
9 

1.05101005 
1.06152015 
1.07213535 
1.08285671 
1.09368527 

1.06408215 
1.07738318 
1.09085047 
1.10448610 
1.11829218 

1.07728400 
1.09344326 
1.10984491 
1.12649259 
1.14338998 

1.10408080 
1.12616242 
1.14868567 
1.17165938 
1.19509257 

1.11767769 
1.14282544 
1.16853901 
1.19483114 
1.22171484 

1.13140821 
1.15969342 
1.18868575 
1.21840290 
1.24886297 

10 
11 
12 
13 
14 

1.10462213 
1.11566835 
1. 12682503* 
1.13809328 
1.14947421 

1.13227083 
1.14642422 
1.16075452 
1.17526395 
1.18995475 

1.16054083 
1.17794894 
1.19561817 
1.21355244 
1.23175573 

1.21899442 
1,24337431 
1.26824179 
1.29360663 
1.31947876 

1.24920343 
1.27731050 
1.30604999 
1.33543611 
1.36548343 

1.28008454 
1.31208666 
1.34488882 
1.37851104 
1.41297382 

15 
16 
17 

18 
19 

1.16096896 
1.17257864 
1.18430443 
1.19614748 
1.20810895 

1.20482918 
1.21988955 
1.23513817 
1.25057739 
1.26620961 

1.25023207 
1.26898555 
1.28802033 
1.30734064 
1.32695075 

1.34586834 
1.37278571 
1.40024142 
1.42824625 
1.45681117 

1.39620680 
1.42762146 
1.45974294 
1.49258716 
1.52617037 

1.44829817 
1.48450562 
1.52161826 
1.55965872 
1.59865019 

20 
21 
22 
23 
24 

1.22019004 
1.23239194 
1.24471586 
1.25716302 
1.26973465 

1.28203723 
1.29806270 
1.31428848 
1.33071709 
1.34735105 

1.34685501 
1.36705783 
1.38756370 
1.40837715 
1.42950281 

1.48594740 
1.51566634 
1.54597967 
1.57689926 
1.60843725 

1.56050920 
1.59502066 
1.63152212 
1.66823137 
1.70576658 

1.63861644 
1.67958185 
1.72157140 
1.76461068 
1.80872595 

25 
26 
27 
28 
29 

1.28243200 
1.29525631 
1.30820888 
1.32139097 
1.33450388 

1.36419294 
1.38124535 
1.39851092 
1.41599230 
1.43369221 

1.45094535 
1.47270953 
1.49480018 
1.51722218 
1.53998051 

1.64060599 
1.67341811 
1.70688648 
1.74102421 
1.77584469 

1.74414632 
1.78338962 
1.82351588 
1.86454499 
1.90G49725 

1.85394410 
1.90029270 
1.94780002 
1.99649502 
2.04640739 

ERIOE 

IS   3% 

35^% 

4% 

iy2% 

5% 

6% 

0 

1 
1 

3 
4 

1. 

1.03 

1.0609 

1.092727 

1.12550881 

1. 

1.035 
1.071225 
1.10871788 
1.14752300 

1. 

1.04 

1.0816 

1.124864 

1.16985856 

1. 

1.045 
1.092025 
1.14110613 
1.19251860 

1. 

1.05 
1.1025 
1.157625 
1.21550625 

1. 

1.06 

1.1236 

1.191016 

1.26247696 

5 

6 
7 
8 
9 

1.15927407 
1.19405230 
1.22987387 
1.20677008 
1.30477318 

1.18768631 
1.22925533 
1.27227920 
1.31680904 
1.36280735 

1.21665290 
1.26531902 
1.31593178 
1.36856905 
1.42331181 

1.24618194 
1.30226012 
1.36086183 
1.42210061 
1.48609514 

1.27628156 
1.34009564 
1.40710042 
1.47745544 
1.55132822 

1.33822558 
1.41851911 
1.50363026 

1.59384807 
1.68947896 

10 
11 
12 
13 
14 

1.34391638 
1.38423387 
1.42576089 
1.46853371 
1.51258972 

1.41059876 
1.45996972 
1.51106866 
1.56395606 
1.61869452 

1.48024428 
1.53945406 
1.60103222 
1.66507351 
1.73167645 

1.55296942 
1.62285305 
1.69588143 
1.77219610 
1.85194492 

1.62889463 
1.71033936 
1.79585633 
1.88564914 
1.97993160 

1.79084770 
1.89829856 
2.01219647 
2.13292826 
2.26090396 

15 
16 
17 

18 
19 

1.55796742 
1.60470644 
1.65284763 
1.70243306 
1.75350605 

1.67534883 
1.73398604 
1.79467555 
1.85748920 
1.92250132 

1.80094361 
1.87298125 
1.94790050 
2.02581652 
2.10684918 

1.93528244 
2.02237015 
2.11337681 

2.20847877 
2.30786031 

2.07892818 
2.18287459 
2.29201832 
2.40661923 
2.52695020 

2.39655819 
2.54035168 
2.69277279 
2.85433915 
3.02559950 

20 
21 
22 
23 
24 

1.80611123 
1.86029457 
1.91610341 
1.97358651 
2.03279411 

1.98978886 
2.05943147 
2.13151158 
2.20611448 
2.28332849 

2.19112314 

2.27876807 
2.36991879 
2.46471554 
2.56330416 

2.41171402 
2.52024116 
2.63365201 
2.75216635 
2.87601383 

2.65329771 
2.78596259 
2.92526072 
3.07152376 
3.22509994 

3.20713547 
3.39956360 
3.60353742 
3.81974966 
4.04893464 

25 
26 
27 
28 
29 

2.09377793 
2.15659127 
2.22128901 
2.28792768 
2.35656551 

2.36324498 
2.44595856 
2.53156711 
2.62017196 
2.71187798 

2.66583633 
2.77246978 
2.88336858 
2.99870332 
3.11865145 

3.00543446 
3.14067901 
3.28200956 
3.42969999 
3.58403649 

3.38635494 
3.55567269 
3.73345632 
3.92012914 
4.11613560 

4.29187072 
4.54938296 
4.82234594 
5.11168670 
5.41838790 

Annuity  Studies 


CHAPTER  I. 

Rules,  Formulas  and  Typical  Problems 

A.  ACCUMULATION  OF  AN  AMOUNT 

Rule: 

The  accumulation  of  $1.00  at  interest  is  found  by  multiplying 
one  plus  the  rate  by  itself  as  many  times,  less  one,  as  there  are 
periods. 

Formula: 

(l+r)» 

Typical  Problem: 

Required  the  accumulation  of  $200.00  in  10  years  @  4%. 

B.  COMPOUND  INTEREST 

Rule: 

The  compound  interest  on  $1.00  is  found  by  multiplying  one 
plus  the  rate  by  itself  as  many  times,  less  one,  as  there  are  periods, 
and  then  subtracting  the  principal,  one. 

Formula: 

(l+r)°-l 

Typical  Problem: 

Required  the  compound  interest  on  $500.00  for  4  years  @  6%. 

7 


C.     PRESENT  WORTH  OF  AN  AMOUNT 

Rule: 

The  present  worth  of  $1.00  is  found  by  dividing  one  by  the 
accumulation  of  $1.00  at  compound  interest  (A). 

Formula: 

1 


(l+r)° 

Typical  Problem: 

Required  the  present  worth  of  $1,000.00  due  4  years  hence, 
money  being  worth  5%. 


D.     DISCOUNT  ON  AN  AMOUNT 

Rule: 

The  discount  is  found  by  subtracting  the  present  worth  (C) 
from  the  principal. 

Formula: 

1 
1  — 


Typical  Problem: 

Required  the  discount  on  $500.00  due  in  3  years  at  5%. 


E.     ACCUMULATION  OF  AN  ANNUITY 

Rule: 

The  accumulation  of  an  annuity  of  $1.00  is  found  by  dividing 
the  compound  interest  (B)  by  the  rate  of  nominal  interest. 

Formula: 

{1+rY-l 

r 
8 


Typical  Problem: 

What  will  be  the  accumulation  of  $200.00  per  year  in  4  years 
at  3%. 


F.     PRESENT  WORTH  OF  AN  ANNUITY 

Rule: 

The  present  worth  of  an  annuity  is  found  by  dividing  the 
discount  (D)  by  the  rate  of  nominal  interest. 

Formula: 

1 

1 


(1+r)'^ 


r 
Typical  Problem: 

Required  the  present  worth  of  an  annuity  of  $200.00  per  year 
with  4  years  to  run  at  3%. 


G.     AMOUNT  OF  AN  ANNUITY  (SINKING  FUND) 

Rule: 

The  amount  of  an  annuity,  or  the  sinking  fund,  which  will 
produce  one  dollar  is  found  by  dividing  the  nominal  interest  by 
the  compound  interest   (B). 

Formula: 


(l+r)°-l 

Typical  Problem: 

Required  the  amount  of  a  sinking  fund  which  will  produce 
$540.00  in  3  years  at  6%. 

9 


H.  RENT  OF  AN  ANNUITY.  (The  amount  which,  when 
periodically  applied  to  an  interest  bearing  principal,  will 
amortize  it  in  a  given  time.) 

Rule: 

To  find  the  rent  of  an  annuity  of  $1.00,  divide  the  rate  by 
the  discount  (D). 

Formula: 


1  — 


in 


(l+r)- 
Typical  Problem: 

"A"  owes  $10,000.00  with  interest  at  6%.  What  uniform 
amount  should  he  pay  annually  for  5  years  to  cover  the  obligation  ? 

I.     PREMIUM  OR  DISCOUNT 

Rule: 

To  find  the  premium  or  discount  on  a  $1.00  bond  or  similar 
obligation : 

(a)  Divide  the  difiFerence  between  the  nominal  and  efifective 
rates  of  interest  by  the  effective  rate  and  multiply  by  the  dis- 
count (D). 

Formula: 

Premium : 

nr — er    /  1 


0 — —) 

\         ri4-er~)°    / 


er         \         (1+er)' 
Discount : 

er — nr    /  1 


(' — —) 


er         V  (1+er)' 

Typical  Problem: 

Premium:    A  5%  bond,  with  2  years  to  run,  is  sold  to  net 
the  investor  4%%.     What  is  the  premium? 

Discount:     A  4%%  bond,  with  4  years  to  run,  is  sold  to 
net  the  investor  5%.    What  is  the  discount? 

10 


J.     RESIDUAL  VALUE 

Rule: 

The  amount  to  which  a  given  amount  may  be  reduced  in  a 
given  number  of  periods  at  a  given  rate  is  found  by  subtracting 
the  rate  from  one ;  raising  the  remainder  to  the  power  equivalent 
to  the  number  of  periods,  and  multiplying  by  the  given  amount. 

Formula: 

A(l— r)° 
Typical  Problem: 

What  is  the  residual  value  of  a  machine  costing  $1200.00 
depreciated  at  10%  on  reducing  balances  for  5  years? 


K.     RATE  OF  REDUCTION,  OR  DEPRECIATION 

Rule: 

The  rate  which  will  reduce  a  given  amount  to  a  lesser  amount 
(residual)  in  a  given  number  of  periods  is  found  by  dividing  the 
residual  by  the  given  amount  and  extracting  the  root  equivalent 
to  the  number  of  periods,  then  subtracting  this  amount  from  one. 

Formula: 


1       n/     R 

Typical  Problem: 

An  automobile  costing  $2,000.00  has  a  life  of  3  years  and  a 
residual  value  of  $1,024.00.  What  is  the  rate  of  depreciation  on 
decreasing  balances? 


11 


CHAPTER  II. 

Illustrative  Problems. 

GROUP  I. 

1.  If  money  is  worth  6%,  what  will  $3,000  amount  to  in  4 
years  if  the  interest  is  collected  semi-annually  and  re-invested 
promptly  ? 


2.    What  is  the  present  worth  of  $30,000  payable  in  4  years 
if  money  is  worth  6%? 


3.  If  you  receive  an  annuity  of  $10,000  per  year,  payable 
annually  at  the  end  of  each  year,  how  much  would  you  have  at 
the  end  of  3  years  provided,  however,  that  the  3rd  payment  had 
not  been  received  and  that  you  had  re-invested  the  money  as  soon 
as  received  at  5%  annually? 


4.    If  money  is  worth  6%,  what  is  the  value  of  an  annuity 
of  $2,000  with  4  years  to  run? 


5.    What  is  the  present  worth  of  $18,000  due  in  5  years  at 
4%? 

12 


GROUP  II. 


1.     What  is  the  residual  value  of  a  machine  costing  $4,000.00 
in  5  years  at  10%? 


2.    What  is  the  residual  value  of  a  machine  costing  $3,000.00 
in  4  years  at  15%  ? 


3.  The  Smith  Manufacturing  Company  acquires  an  auto- 
mobile for  $1,500.00.  They  anticipate  trading  it  in  on  another 
machine  in  2  years  at  a  value  of  $486.00.  What  is  the  rate  of 
depreciation  on  decreasing  balances? 


4.     Suppose  the  cost  was  $4,000.00  and  the  residual  value 
$1,687.50. 


5.  Which  is  the  better  purchase,  and  what  is  the  saving 
during  each  of  the  first  3  years,  on  a  machine  costing  $2,000.00 
with  a  4  years  life  and  a  residual  value  of  $819.20,  over  a  machine 
costing  $1,800.00  having  a  3  years  life  with  a  residual  value  of 
$1029.22. 

13 


GROUP  III. 


1.  Jno.  Smith  has  an  obligation  of  $19,500.20  due  2  years 
hence.  What  amount  should  he  invest  at  intervals  of  six  months 
in  order  to  accumulate  the  desired  amount  if  he  is  able  to  secure 
5%  interest  on  his  investment? 


2.  Jones  is  entitled  to  an  annuity  of  $50,000  per  year  for 
two  years  payable  in  quarterly  installments.  How  much  would 
you  be  willing  to  pay  for  this  annuity  if  money  were  worth  5% 
and  the  next  installment  were  due  3  months  from  today? 


3.  An  arrangement  is  made  whereby  $15,000  is  deposited 
every  six  months  in  a  trust  company  at  3%  interest.  Provided 
that  these  deposits  are  continued  for  8  periods,  what  would  be 
the  amount  of  the  sinking  fund? 


4.    What  is  the  present  worth  of  $1,000  due  in  6  years  at  6%  ? 


5.  What  is  the  present  worth  of  the  interest  which  would  be 
received  on  five  $1,000  bonds  bearing  6%  interest,  due  in  4  years 
if  money  is  worth  6%? 

14 


GROUP   IV. 


1.  The  John  Doe  Investment  Company  contemplates  loan- 
ing approximately  $20,000  to  the  Appleby  Manufacturing  Co. 
and  receiving  therefrom  $1,000,  5%  gold  bonds.  They  desire  a 
return  of  6%  on  their  money;  what  is  the  exact  amount  they  will 
loan  which  will  nearest  equal  $20,000  and  how  many  bonds  will 
they  receive?    Time,  10  years. 


2.  Which,  if  either  of  the  following  amounts  correctly  rep- 
resent the  value  of  ten  4%%  bonds  due  in  3  years  on  a  4%  basis, 
interest  payable  semi-annually?     A,  $10,138.75;  B,  $9,859.96. 


3.  (a)  What  premium  should  be  paid  on  five  $1,000  bonds 
maturing  in  3  years  with  interest  at  5%  payable  semi-annually  on  a 
4%'%  basis  ? 


(b)   How  much  would  be  the  discount  on  a  6%  basis? 


(c)  Suppose  that  the  bonds  bore  4%  interest,  payable  semi- 
annually, what  would  be  the  amount  of  the  discount  ? 


4.  You  are  offered  five  $1,000  5%  bonds  payable  in  3  years 
at  1013/8  and  five  $1,000  41/2%  bonds  payable  in  3  years  at  lOli/g. 
Which  is  the  better  purchase,  presuming  that  4i/2%  on  the  first 
group  of  bonds  and  4%  on  the  second  group  of  bonds  are  fair 
rates  of  return  considering  the  nature  of  the  investment  ? 


5.    Prepare  a  table  showing  the  amortization  of  a  6%  bond 
on  a  5%  basis  for  4  years. 

15 


GROUP  V. 

1.  Bonds  due  in  2  years  bearing  6%  interest,  payable  semi- 
annually, and  yielding  S^^"  each  half  year  are  worth  1.01881. 
Prepare  an  amortization  table  showing  the  value  in  this  bond  for 
each  half  year  of  the  two  years. 


2.    Required  the  ledger  accounts  in  detail  to  record  the  fol- 
lowing transactions: 

10,  4%  bonds  are  purchased  on  a  given  date,  just  after  the 
interest  coupons  for  that  date  had  been  removed,  at  87%. 
Nine  months  later  the  bonds  were  sold  for  88^2  ^ynd  interest. 
What  was  the  profit? 


3.  (a)  $5,000  of  4%%  bonds,  interest  payable  semi-annually, 
with  two  years  to  run,  were  purchased  for  $4,850.  The  purchaser 
estimated  that  the  bonds  would  net  him  3%  per  half  year.  To 
what  amount  did  he  err  in  his  estimate? 

(b)  Three  months  later  he  is  offered  97%  and  interest  for 
his  bonds.  Presuming  that  he  sells  the  bonds,  what  entries  will 
be  required  on  his  books. 


4.  A  piece  of  real  property  is  being  sold,  subject,  however, 
to  the  rights  of  a  life  tenant.  The  remainderman  estimates  that 
the  property  is  worth  $10,000.  Presuming  that  the  life  tenant's 
equity  runs  for  6  years  and  that  the  property  produces  6%  on  the 
estimated  value,  what  amount  should  be  paid  to  the  life  tenant  to 
satisfy  both  the  life  tenant  and  the  remainderman  ? 


5.    Given  a  15  year  annuity  of  $60.00,  the  first  payment 
of  which  falls  due  one  year  hence. 

16 


(a)  What  is  the  value  of  the  annuity  at  5%? 

(b)  What   amount   will   accumulate   during  the   period   if 
each  moiety  is  reinvested  as  it  becomes  due. 

Assume  interest  at  the  rate  of  5%,  payable  annually. 


6.  What  amount  will  be  required  to  produce  $20,000  in  10 
years,  provided  $2,000  per  year  has  been  set  aside  for  three  of 
the  10  years  and  that  these  amounts,  with  the  future  annual  pay- 
ments of  the  remaining  7  years,  bear  4%  interest? 


17 


CHAPTER  III. 
General  Problems. 

1.  Required  the  present  worth  of  an  annuity  of  $50.00,  the 
first  payment  of  which  falls  due  one  year  hence  and  continues 
for  25  years.    Interest  5%, 

2.  If  each  moiety  of  the  preceding  question  were  invested 
promptly,  what  would  be  the  accumulation  at  the  end  of  the 
period  ? 

3.  You  have  been  requested  to  advise  the  amount  of  a 
sinking  fund  which  will  produce  $500,000.00  in  25  years,  amounts 
to  be  invested  annually  at  5%.    What  is  the  amount? 

4.  A  corporation  has  outstanding  an  issue  of  20-year  6% 
bonds,  with  10  years  to  run,  which  were  sold  to  net  the  investor 
5%.  They  now  have  an  opportunity  to  buy  $100,000.00  of  these 
bonds  at  102.  Is  it  advisable  for  them  to  buy?  If  so,  what  will 
they  save,  also  what  entries  should  be  made  on  their  books  of 
account  to  record  the  purchase? 

5.  Under  the  terms  of  an  agreement,  a  debt  of  $100,000.00 
with  interest  at  5%  is  to  be  paid  as  follows:  Nine  equal  annual 
payments  and  a  tenth  payment  of  $12,000.00.  What  is  the  amount 
of  the  annual  payments? 

6.  What  should  be  paid  for  a  6%  bond,  interest  payable 
semi-annually  with  3  years  to  run,  if  it  is  to  net  5%  ? 

7.  What  is  the  present  worth  of  an  annuity  of  $700.00  for 
7  years  at  5%  ? 

8.  Find  the  annuity  whose  amount  for  25  years  at  6%  is 
$16,459.35. 

18 


9.  A  man  bought  a  tract  of  land  for  $4,800.00  which  was 
to  be  paid  in  installments  of  $600.00  per  year.  How  much  money 
at  6%  interest  (compound)  would  discharge  the  debt  at  the  time 
of  purchase? 


10.     Required  the  present  worth  of  the  following  annuities: 
Amount        Periods       Rate 

A.  $500.00  12  2% 

B.  800.00  6  4% 

C.  500.00  11         11/2% 


11.     Ascertain  the  accumulation  of  the  amounts  in  question 
10  at  the  rates  and  for  the  periods  given. 


12.     What  is  the  rent  of  an  annuity  of  15  periods,  if  the 
present  worth  is  $1,200.00  and  the  rate  11/2%? 


13.     What   amount,   set   aside   semi-annually,   will   produce 
$1,000.00  in  12  years  at  4%  interest? 


14.     If  interest  at  6%  per  annum  is  paid  monthly,  what  is 
the  effective  rate? 


15.  If  a  person  receives  $15.00  per  quarter  on  $1,000.00, 
what  is  the  effective  rate  of  interest  per  annum? 

16.  Which  is  the  more  valuable  and  how  much:  $8,160.00 
payable  annually  or  $2,000.00  each  quarter,  interest  5%  ? 

17.  If  money  is  worth  5%  per  annum,  what  rate  should  be 
quoted  where  payments  are  to  be  made  quarterly? 

18.  If  a  4%  bond  nets  2%%  semi-annually  what  is  its  value 
— 5  years  to  run? 

19 


19.     As  above,  but  3%  netting  2%%  semi-annually — 7  years 
to  run? 


20.     Same  as  above,  but  5%  netting  6%  annually — 12  years 
to  run. 


21.  Same  as  No.  20  but  netting  3%%  semi-annually? 

22.  Prepare  a  table  showing  the  annual  book  values  and 
the  amortization  of  a  6%  bond  netting  2^/2%  semi-annually — 9 
years  to  run. 

23.  On  March  1st,  1918,  $30,000.00  3%  bonds,  due  July 
1st,  1920,  J.  &  J.,  were  sold,  netting  4%.    What  is  the  price  flat? 

24.  What  are  the  intermediate  payments  on  an  obligation 
of  $200,000.00  bearing  6%  interest,  payable  $20,000.00  cash:  9 
equal  annual  payments  and  a  final  payment  in  10  years  of  $8,000.00. 


25.     If,  in  question  24,  the  final  payment  had  been  $28,000.00, 
what  would  have  been  the  amount  of  the  9  intermediate  payments  ? 


26.  What  will  be  the  residual  value  of  a  machine  costing 
$5,000.00  with  an  estimated  life  of  12  years,  depreciated  at  15% 
annually  ? 


27.     What  rate  should  be  used  in  problem  No.  26  to  produce 
a  residual  value  of  $1,315.00  in  10  years? 


28.  What  is  the  bid  on  $100,000.00  5%  bonds  maturing 
at  the  end  of  3  years,  interest  payable  semi-annually,  to  net  the 
purchaser  a  nominal  rate  of  4%  ? 

20 


29.  What  is  the  bid  on  $100,000.00  3%  bonds  maturing  at 
the  end  of  6  years,  interest  payable  semi-annually,  to  net  the 
purchaser  a  nominal  rate  of  4%  ? 

30.  On  August  1st,  1919,  $5,000.00  5%  bonds,  due  April  1st, 
1921,  are  offered  at  prices  to  yield  4%%.  What  is  the  price  "and 
interest"? 


21 


THTfl  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 

AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED   FOR   FAILURE  TO   RETURN 
THIS   BOOK   ON   THE   DATE  DUE.   THE   PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY    AND    TO     $1.00    ON    THE    SEVENTH     DAY 
OVERDUE. 

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NOV  22  mi 

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